Addition and Subtraction of Polynomials :: Galois Field Computations (Communications Toolbox)

Communications Toolbox

Addition and Subtraction of Polynomials

To add and subtract polynomials, use + and - on equal-length Galois vectors that represent the polynomials. If one polynomial has lower degree than the other, then you must pad the shorter vector with zeros at the beginning so that the two vectors have the same length. The example below shows how to add a degree-one and a degree-two polynomial.

lin = gf([4 2],3); % A^2 x + A, which is linear in x
linpadded = gf([0 4 2],3); % The same polynomial, zero-padded
quadr = gf([1 4 2],3); % x^2 + A^2 x + A, which is quadratic in x
% Can't do lin + quadr because they have different vector lengths.
sumpoly = [0, lin] + quadr; % Sum of the two polynomials
sumpoly2 = linpadded + quadr; % The same sum

Polynomials over Galois Fields

Multiplication and Division of Polynomials